Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Average Error: 11.9 → 2.4

Time: 9.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{x \cdot \left(y - z\right)}{t - z}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r751939 = x;
        double r751940 = y;
        double r751941 = z;
        double r751942 = r751940 - r751941;
        double r751943 = r751939 * r751942;
        double r751944 = t;
        double r751945 = r751944 - r751941;
        double r751946 = r751943 / r751945;
        return r751946;
}

↓

double f(double x, double y, double z, double t) {
        double r751947 = z;
        double r751948 = -9.512737302380148e-222;
        bool r751949 = r751947 <= r751948;
        double r751950 = 5.4381737647266115e-107;
        bool r751951 = r751947 <= r751950;
        double r751952 = !r751951;
        bool r751953 = r751949 || r751952;
        double r751954 = x;
        double r751955 = y;
        double r751956 = r751955 - r751947;
        double r751957 = t;
        double r751958 = r751957 - r751947;
        double r751959 = r751956 / r751958;
        double r751960 = r751954 * r751959;
        double r751961 = r751954 / r751958;
        double r751962 = r751961 * r751956;
        double r751963 = r751953 ? r751960 : r751962;
        return r751963;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	11.9
Target	2.2
Herbie	2.4

\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

1. Split input into 2 regimes

2. if z < -9.512737302380148e-222 or 5.4381737647266115e-107 < z

   1. Initial program 13.3

      \[\frac{x \cdot \left(y - z\right)}{t - z}\]
   2. Using strategy rm

   3. Applied *-un-lft-identity 13.3

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot \left(t - z\right)}}\]

   4. Applied times-frac 1.2

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{t - z}}\]

   5. Simplified 1.2

      \[\leadsto \color{blue}{x} \cdot \frac{y - z}{t - z}\]

   if -9.512737302380148e-222 < z < 5.4381737647266115e-107

   1. Initial program 6.7

      \[\frac{x \cdot \left(y - z\right)}{t - z}\]
   2. Using strategy rm

   3. Applied *-un-lft-identity 6.7

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot \left(t - z\right)}}\]

   4. Applied times-frac 5.5

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{t - z}}\]

   5. Simplified 5.5

      \[\leadsto \color{blue}{x} \cdot \frac{y - z}{t - z}\]
   6. Using strategy rm

   7. Applied pow1 5.5

      \[\leadsto x \cdot \color{blue}{{\left(\frac{y - z}{t - z}\right)}^{1}}\]

   8. Applied pow1 5.5

      \[\leadsto \color{blue}{{x}^{1}} \cdot {\left(\frac{y - z}{t - z}\right)}^{1}\]

   9. Applied pow-prod-down 5.5

      \[\leadsto \color{blue}{{\left(x \cdot \frac{y - z}{t - z}\right)}^{1}}\]

   10. Simplified 6.9

       \[\leadsto {\color{blue}{\left(\left(y - z\right) \cdot \frac{x}{t - z}\right)}}^{1}\]
3. Recombined 2 regimes into one program.

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.5127373023801481 \cdot 10^{-222} \lor \neg \left(z \le 5.43817376472661147 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))